You could always quit the mission and keep the golf ball. It's just a cheap plastic "whiffle" type one, not a real one though if that makes a difference. We had a lot of trouble with this one. Went to the phone and while it said a golf ball would drop into the slot, one didn't. We went to the next step and tried to continue but it wouldn't without the golf ball. Went back to the station near IG and they gave us a golf ball. But when we went back, the "cleaner" would no longer open since it showed it already had for us. So we still couldn't continue. We just went back to the station again and gave them both the phone and golf ball. It has worked for us on another occasion but if you really want the golf ball, you'd just need to stop and get a new F.O.N.E.
As far as splitting - I know with us they've always kind of pushed us to do it together, even with 4 people. I think they only have a limited number of the devices that stay charged and work at any location (and a couple times they've died on us before we finished a mission). If your kids are older, you could easily just sign up separately (pretending they weren't together). But I think it would be more fun for them to do it together and just take turns and certainly easier to keep an eye on the younger kids. Most of the things that happen have an "I missed it; show it again" button so if something cool happened (we love the Japan one where Perry zips out on a motorboat), both of them could click it once and see it happen.
One recent change (in the last few months) is that you no longer have to listen to all of the story line if you're mostly interested in just seeing the cool things happen around the country you're in. If you're a P&F fan, it's definitely worth doing the stories but if your kids are too young to know them or as an adult you're not familiar with them, you can just hit "skip" every time it comes up and then the whole mission would take about 10 minutes. I will say though that playing Agent P is what got me (as a 50ish adult) to watch all the P&F episodes! My running playlist these days is almost exclusively made up of their songs (and my kids are all in their 20's).
Just one more note - the Mexico mission is completely indoors inside the pyramid so makes a great one to do either during a thunderstorm or when it's crazily hot in the afternoon (while parents hit La Cava!). As a whole, these missions are much more fun to do in January than July. We did France this past Saturday around 1pm and it was just miserable. (We did get a pressed penny though).